Frequency Scales for Current Statistics of Mesoscopic Conductors

Nagaev, K. É.; Pilgram, Sebastian; Büttiker, Μ.

doi:10.1103/physrevlett.92.176804

Cited by 54 publications

(62 citation statements)

References 19 publications

(20 reference statements)

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“…13,14 A powerful and elegant formulation in this semiclassical regime is the stochastic path integral approach, which was introduced for FCS in the pioneering works by Pilgram et al [15][16][17] For interacting systems, the FCS can be related to a generalized master equation describing the charge transport [18][19][20][21] or obtained using Keldysh Greens functions.…”

Section: 10-12mentioning

confidence: 99%

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Factorial cumulants reveal interactions in counting statistics

2011

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Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent singleparticle events, and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.

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Section: 10-12mentioning

confidence: 99%

“…3a we show the asymptotic expression [Eq. (17)], taking into account the three singularities that are closest to z = 0 [indicated by filled red circles in Fig. 3(b)].…”

Section: Low Biasmentioning

confidence: 99%

Factorial cumulants reveal interactions in counting statistics

2011

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“…[11][12][13] As far as the frequency dependence of the higher cumulants is concerned, the situation changes drastically as compared to conventional noise spectra. Calculations of the frequency-dependent third cumulant for a chaotic cavity 8 and for a diffusive conductor 14 show marked differences from the conventional noise: it is not only determined by the charge-relaxation time but also shows a low-frequency dispersion that is determined by the dwell time D .…”

Section: Introductionmentioning

confidence: 99%

“…6 and 7. Recent calculations of current noise in chaotic cavities 8,9 that take both the energydependence of scattering and Coulomb interactions into account show that the frequency-dependent noise spectrum is determined solely by the time , as long as quantum corrections such as weak-localization can be ignored.…”

Section: Introductionmentioning

confidence: 99%

Frequency-dependent current correlation functions from scattering theory

Salo

Hekking

Pekola³

2006

Phys. Rev. B

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We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal with arbitrary correlation functions. The formalism proves useful, e.g., in view of recent developments in full counting statistics of charge transfer, where detecting schemes have been proposed for measurement of frequency dependent spectra of higher moments. Some of these schemes are different from the well-known fictitious spin detector and therefore generally involve calculation of non-Keldysh-contourordered correlation functions. As an illustration of the approach we consider various third order correlation functions of current, including the usual third cumulant of current statistics. We investigate the frequency dependence of these correlation functions explicitly in the case of energy-independent scattering. The results can easily be generalized to the calculation of arbitrary nth order correlation functions, or to include the effect of interactions.

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“…9 Moreover, the recent rise of interest in the full counting statistics of charge transfer has led to a reexamination of the frequency noise spectra. [10][11][12] This experimental progress has since triggered renewed theoretical interest in time-dependent mesoscopic transport. [13][14][15][16][17][18] One way to tackle the ac-transport problem is to start from linear-response theory for a given potential distribution of the sample.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical approach to the ac conductance of chaotic cavities

et al. 2009

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We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime.

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Frequency Scales for Current Statistics of Mesoscopic Conductors

Cited by 54 publications

References 19 publications

Factorial cumulants reveal interactions in counting statistics

Factorial cumulants reveal interactions in counting statistics

Frequency-dependent current correlation functions from scattering theory

Semiclassical approach to the ac conductance of chaotic cavities

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